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Pascals triangle problem(discrete mathematics)

  1. Oct 28, 2012 #1
    1. The problem statement, all variables and given/known data
    Determine which row of pascals triangle contains 3 consecutive entries that are in the ratio 1:2:3.

    2. Relevant equations
    (n, k ) = n!/k!(n-k)!


    3. The attempt at a solution
    (n,k):(n,k+1):(n,k+2)
    1 : 2: : 3

    What I did was cross multiply.

    2 times (n,k) = 1 times (n,k+1) and 3 times (n,k+1) = 2 times (n,k+2)
    2(n!/(k!(n-k)!) = n!/(k+1)!(n-k-1)! and 3(n!/(k+1)!(n-k-1)!) = 2(n!/(k+2)!(n-k-2)!

    I know that i should solve for n in the first equation then substitute n in the second equation to get n and k. I'm stuck on the algebra part.
     
  2. jcsd
  3. Oct 28, 2012 #2

    Mentallic

    User Avatar
    Homework Helper

    Well, what are some of the rules of factorials?

    n! = n*(n-1)*(n-2)*...*2*1

    n! = n*(n-1)!

    So if we have an equation such as

    n! = 10*(n-1)!

    then to solve this, we would use the rule n! = n*(n-1)! to obtain

    n*(n-1)! = 10*(n-1)!

    then you can divide through by (n-1)! and find n=10. See if you can apply this rule to solve your equation.
     
  4. Oct 30, 2012 #3
    thank you i got the answer.
     
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